The Binomial Theorem

Binomial Theorem and its Applications

Binomial Expansion of  $\left(1+b\right)^n$  

Why learn Binomial Theorem?

https://youtu.be/nYO2DqoZdd4

Introductory Problem

Page 80 Textbook

Pascal's Triangle

Student Learning Space

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Open Ended

What is the link between Pascal's Triangle and Binomial Expansion?

Multiple Choice

How many terms are the in the expansion of (1+b)⁵

• 5

• 6

• 25

• 50

• 3

Multiple Choice

What is the Binomial expansion of (x + 1)⁵ ?

• x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

• x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

• x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

• x⁵ + 1

Multiple Choice

Select the correct expansion of

(1 - x)⁵

• 1 − 5x + 10x² − 10x³ + 5x⁴ − x⁵

• 1 + 5x + 10x² + 10x³ + 5x⁴ + x⁵

• -1 + 5x - 10x² + 10x³ - 5x⁴ + x⁵

• 1 − 5x + 10x² + 10x³ + 5x⁴ − x⁵

Multiple Choice

Select the correct expansion of

(1 + 4x)³

• 1 + 12x + 12x² + 4x³

• 1 + 12x + 48x² + 64x³

• 1 + 3x + 3x² + x³

• 1 + 4x + 16x² + 64x³

Multiple Choice

Find the 2nd term in the expansion of

(2b + 1)³

• 12b²

• 6b

• 8b³

• 4b²

Poll

Are you able to apply Pascal's Triangle to Binomial expansion questions confidently?

• 100% Yes

• 75% Yes

• 50% Yes

• 25% Yes

• 100%No

Homework - Class Practice - Foolscap Paper

Page 87 Ex 5A Q1, Q2 and Q3

Binomial Coefficients

Investigation

Page 82 Textbook

Student Learning Space

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Multiple Choice

Find the value of...

₈C₅

• 56

• 70

• 8

• 28

Multiple Choice

Find the coefficient of x³ in the expansion of (1 + x)²⁰

• 1140

• 190

• 4845

• 8000

Multiple Choice

Find the coefficient of x⁴ in the expansion of (1 - x)¹⁴

• 1001

• -1001

• 364

• -364

Multiple Choice

Find the coefficient of x² in the expansion of (1 + 4x)⁹

• 576

• 36

• 144

• 1344

Multiple Choice

Find the coefficient of y³ in the expansion of (1 - 3y)¹⁴

• -9828

• 9828

• 364

• -364

Poll

Are you able to apply the n! and nCr to Binomial expansion questions confidently?

• 100% Yes

• 75% Yes

• 50% Yes

• 25% Yes

• 100%No

Homework - Class Practice - Foolscap Paper

Page 87 Ex 5A Q4 to Q12